Subgroup temperaments: Difference between revisions

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 == 2.3.… subgroups ==
 === Shrub ===
-This is a restriction of diaschismic which omits the tritone to produce a diatonic scale. True to its name, it generates a [[shrubmajor]] third (~425c) in quarter-comma tuning.
+Shrub is a [[restriction]] of [[diaschismic family #Diaschismic|diaschismic]] which omits the tritone to produce a [[5L 2s|diatonic]] scale. True to its name, it generates a [[neogothic major and minor|shrubmajor]]{{idio}} third (~425{{c}}) in quarter-comma tuning. It has an equal-temperament join of 12 & 17.
-Subgroup: 2.3.25
+==== 2.3.25 subgroup ====
+[[Subgroup]]: 2.3.25
-Edo join: 17 & 12
+[[Comma list]]: 2048/2025
-Comma list: [[2048/2025]]
+{{Mapping|legend=3| 1 0 11 | 0 1 -4 }}
+: mapping generators: ~2, ~3
-{{Mapping|legend=3| 1 1 7| 0 1 -4}}
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1198.8214{{c}}, ~3/2 = 704.2059{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.9585{{c}}
-Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.136
+{{Optimal ET sequence|legend=1| 12, 17, 46, 63, 80, 143* }}
-==== 2.3.23.25.41 subgroup ====
+<nowiki/>* Wart for 25
-''See also: [[Reversed meantone]]''
-Edo join: 17 & 12
+[[Badness]] (Sintel): 0.234
-Comma list: 2048/2025, 576/575, 82/81
+===== 2.3.25.23 subgroup =====
+Subgroup: 2.3.25.23
-{{Mapping|legend=3| 1 1 1 7 3| 0 1 6 -4 4}}
+Comma list: 576/575, 736/729
-Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 705.264
+{{Mapping|legend=2| 1 0 11 -5 | 0 1 -4 6 }}
-===== Sburb =====
+Optimal tunings:
-This temperament sets the [[octave reduction|octave-reduced]] 413th harmonic (413/256, 827.998{{c}}) to the diminished seventh.
+* WE: ~2 = 1198.9504{{c}}, ~3/2 = 704.6585{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.1888{{c}}
-Subgroup: 2.3.7.23.25.41.59
+{{Optimal ET sequence|legend=0| 12, 17, 63, 80, 97*, 114* }}
-Edo join: 17 & 12
+<nowiki/>* Wart for 25
-Comma list: 64/63, 225/224, 162/161, 82/81, 177/175
+Badness (Sintel): 0.223
-{{Mapping|legend=3| 1 1 4 1 7 3 10| 0 1 -2 6 -4 4 -7}}
+===== 2.3.25.23.41 subgroup =====
+{{See also| Reversed meantone }}
-Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 706.387
+Subgroup: 2.3.25.23.41
+Comma list: 82/81, 369/368, 576/575
+{{Mapping|legend=2| 1 0 11 -5 -1 | 0 1 -4 6 4 }}
+Optimal tunings:
+* WE: ~2 = 1199.3246{{c}}, ~3/2 = 705.2238{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 705.5491{{c}}
+{{Optimal ET sequence|legend=0| 5, 12, 17 }}
+Badness (Sintel): 0.284
+==== Sburb ====
+Sburb is every other step of [[pajara]], extended to the add-23 add-41 subgroup in the same way as shrub. It can also admit a [[59/1|59th harmonic]] by setting the [[octave reduction|octave-reduced]] 413th harmonic (413/256, 827.998{{c}}) to the diminished seventh.
+Subgroup: 2.3.25.7
+Comma list: 50/49, 64/63
+{{Mapping|legend=2| 1 0 11 6 | 0 1 -4 -2 }}
+Optimal tunings:
+* WE: ~2 = 1197.6967{{c}}, ~3/2 = 705.6906{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 707.3438{{c}}
+{{Optimal ET sequence|legend=0| 5, 12, 17, 39d }}
+Badness (Sintel): 0.253
+===== 2.3.25.7.23 subgroup =====
+Subgroup: 2.3.25.7.23
+Comma list: 50/49, 64/63, 162/161
+{{Mapping|legend=2| 1 0 11 6 -5 | 0 1 -4 -2 6 }}
+Optimal tunings:
+* WE: ~2 = 1197.5577{{c}}, ~3/2 = 705.3089{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 706.7010{{c}}
+{{Optimal ET sequence|legend=0| 5, 12, 17 }}
+Badness (Sintel): 0.419
+===== 2.3.25.7.23.41 subgroup =====
+Subgroup: 2.3.25.7.23.41
+Comma list: 50/49, 64/63, 82/81, 162/161
+{{Mapping|legend=2| 1 0 11 6 -5 -1 | 0 1 -4 -2 6 4 }}
+Optimal tunings:
+* WE: ~2 = 1197.9403{{c}}, ~3/2 = 705.9522{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 707.0779{{c}}
+{{Optimal ET sequence|legend=0| 5, 12, 17, 39d }}
+Badness (Sintel): 0.450
 === Darian calendar ===